On existence and uniqueness for transport equations with non-smooth velocity fields under inhomogeneous Dirichlet data

DOI IR (HANDLE) Open Access

Description

A transport equation with a non-smooth velocity field is considered under inhomogeneous Dirichlet boundary conditions. The spatial gradient of the velocity field is assumed in Lp′in space and the divergence of the velocity field is assumed to be bounded. By introducing a suitable notion of solutions, it is shown that there exists a unique renormalized weak solution for Lp initial and boundary data for 1/p+1/p′ = 1. Our theory is considered as a natural extension of the theory due to DiPerna and Lions (1989), where there is no boundary. Although a smooth domain is considered, it is allowed to be unbounded. A key step is a mollification of a solution. In our theory, mollification in the direction normal to the boundary is tailored to approximate the boundary data.

Journal

Keywords

Details 詳細情報について

  • CRID
    1390303000764753920
  • DOI
    10.14943/112379
  • HANDLE
    2115/93942
  • Text Lang
    en
  • Article Type
    departmental bulletin paper
  • Data Source
    • JaLC
    • IRDB
  • Abstract License Flag
    Allowed

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